See the attachment.
If you have trouble visualising the curve you can see the animation
motion on a saddle on my web site Calculus 3
Let i + j + k, and be the curve of intersection of the hyperbolic paraboloid and the cylinder oriented counterclockwise as viewed from above.
(i) Obtain a parametrization of the curve and use the result to evaluate r.
(ii) use Stokes's Theorem to evaluate r.
See the attachment.
If you have trouble visualising the curve you can see the animation
motion on a saddle on my web site Calculus 3